Mini course on Statistics in Astronomy (2013)


Jan 25–Feb 15: F11, AB 113; after reading week: TBD.
Barth Netterfield and Marten van Kerkwijk
Web page
Course texts
As given below, but a general reference would be Bayesian Logical Data Analysis for the Physical Sciences (BLDAPS), by Phil Gregory (2005, Cambridge Univ. Press). This text also describes non-Bayesian analysis and shows how for quite general cases the results are very similar. See also a pdf scan of Marten's notes.
For students taking this course for credit: the testing will be by two assignments.
  1. Problem set 1 (pdf), due 1 March 2013
  2. To come


Fri, Jan 25 (Marten)

Literature: Numerical Recipes, parts of Chapter 15; BLDAPS 5, 6

  • General error propagation.
  • Introduction to χ2 fitting, probabilities, number of parameters, degrees of freedom. Estimating expected uncertainties.
  • Applications: straight line, etc.

Fri Feb 1 (Barth)

  • Introduction to Bayesian analysis; (1 parameter), priors.
  • Relation with "frequentist" approach.

Fri Feb 8 (Marten;

Literature: Horne 1986PASP…98..609H: An optimal extraction algorithm for CCD spectroscopy.

  • Determining the optimal way to extract data; thinking clearly about what is actually measured.
  • Application to images and spectra.

Fri Feb 15 (Marten)

Literature: Numerical Recipes, remainder of Chapter 15; Alard & Lupton, 1998ApJ…503..325A: A Method for Optimal Image Subtraction; Rucinski 2002AJ….124.1746R: Radial Velocity Studies of Close Binary Stars. VII. Methods and Uncertainties.

  • General least-squares modelling with base functions.
  • Least-squares fitting algorithms
  • Applications: optimal image subtraction, rotational line profiles

Fri Mar 1 (Barth)

  • Non Gaussian likelihoods and error estimates.
  • Significance estimates.

Fri Mar 8 (Marten)

Literature: Cash 1979ApJ…228..939C: Parameter estimation in astronomy through application of the likelihood ratio; for a Bayesian perspective, Gregory & Loredo 1992ApJ…398..146G: A new method for the detection of a periodic signal of unknown shape and period.

  • Poisson errors, maximum likelihood for Poisson-distributed data.
  • Pitfalls: Resolution and binning (e.g., for X-ray spectra).
  • Pitfalls: number of trials (e.g., source/period finding).

Fri Mar 15 (Barth)

  • Multi Parameter Baysian, Fischer matrix.
  • Correlated parameters, marginalization.

Fri Mar 22 (Barth)

  • Monte Carlo analysis, error estimates.
  • Relation to Baysian analysis.
  • More pitfalls??

Author: Marten van Kerkwijk <>

Date: 2013-02-22 14:32:02 EST

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